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Box plots or box-whisker plots give a good graphical image of the concentration of the data. They also show how far from most of the data the extreme values are. The box plot is constructed from five values: the smallest value, the first quartile, the median, the third quartile, and the largest value. The median, the first quartile, and the third quartile will be discussed here, and then again in the section on measuring data in this chapter. We use these values to compare how close other data values are to them.

The median , a number, is a way of measuring the "center" of the data. You can think of the median as the "middle value," although it does not actually have to be one of the observed values. It is a number that separates ordered data into halves. Half the values are the same number or smaller than the median and half the values are the same number or larger. For example, consider the following data:

  • 1
  • 11.5
  • 6
  • 7.2
  • 4
  • 8
  • 9
  • 10
  • 6.8
  • 8.3
  • 2
  • 2
  • 10
  • 1

Ordered from smallest to largest:

  • 1
  • 1
  • 2
  • 2
  • 4
  • 6
  • 6.8
  • 7.2
  • 8
  • 8.3
  • 9
  • 10
  • 10
  • 11.5

The median is between the 7th value, 6.8, and the 8th value 7.2. To find the median, add the two values together and divide by 2.

6.8 7.2 2 7

The median is 7. Half of the values are smaller than 7 and half of the values are larger than 7.

Quartiles    are numbers that separate the data into quarters. Quartiles may or may not be part of the data. To find the quartiles, first find the median or second quartile. The first quartile is the middle value of the lower half of the data and the third quartile is the middle value of the upper half of the data. To get the idea, consider the same data set shown above:

  • 1
  • 1
  • 2
  • 2
  • 4
  • 6
  • 6.8
  • 7.2
  • 8
  • 8.3
  • 9
  • 10
  • 10
  • 11.5

The median or second quartile is 7. The lower half of the data is 1, 1, 2, 2, 4, 6, 6.8. The middle value of the lower half is 2.

  • 1
  • 1
  • 2
  • 2
  • 4
  • 6
  • 6.8

The number 2, which is part of the data, is the first quartile . One-fourth of the values are the same or less than 2 and three-fourths of the values are more than 2.

The upper half of the data is 7.2, 8, 8.3, 9, 10, 10, 11.5. The middle value of the upper half is 9.

  • 7.2
  • 8
  • 8.3
  • 9
  • 10
  • 10
  • 11.5

The number 9, which is part of the data, is the third quartile . Three-fourths of the values are less than 9 and one-fourth of the values are more than 9.

To construct a box plot, use a horizontal number line and a rectangular box. The smallest and largest data values label the endpoints of the axis. The first quartile marks one end of the box and the third quartile marks the other end of the box. The middle fifty percent of the data fall inside the box. The "whiskers" extend from the ends of the box to the smallest and largest data values. The box plot gives a good quick picture of the data.

You may encounter box and whisker plots that have dots marking outlier values. In those cases, the whiskers are not extending to the minimum and maximum values.

Consider the following data:

  • 1
  • 1
  • 2
  • 2
  • 4
  • 6
  • 6.8
  • 7.2
  • 8
  • 8.3
  • 9
  • 10
  • 10
  • 11.5

The first quartile is 2, the median is 7, and the third quartile is 9. The smallest value is 1 and the largest value is 11.5. The box plot is constructed as follows (see calculator instructions in the back of this book or on the TI web site ):

Questions & Answers

what is economic
Charles Reply
what are the type of economic
Charles
macroeconomics,microeconomics,positive economics and negative economics
Gladys
what are the factors of production
Gladys
process of production
Mutia
Basically factors of production are four (4) namely: 1. Entrepreneur 2. Capital 3. Labour and; 4. Land but there has been a new argument to include an addition one to the the numbers to 5 which is "Technology"
Elisha
what is land as a factor of production
Gladys
what is Economic
Abu
economics is how individuals bussiness and governments make the best decisions to get what they want and how these choices interact in the market
Nandisha
Economics as a social science, which studies human behaviour as a relationship between ends and scarce means, which have alternative uses.
Yhaar
how will a country's population be equal to it's labour force
Hope Reply
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Obeng Reply
What is Economic
Governor Reply
economic
Nwosu
Economics is the social science that deals with the unlimited human wants in the face of scarce (limited in supply) resources.
Azka
what is market
Gift Reply
marker is the interaction of buying and selling
David
market refers to the interaction of the processes of buying and selling of commodities between the buyer and the seller.
stephen
market is a place where two parties gather to facilitate exchange of goods and services.
Yhaar
what are some good sources of information to find trends in various Industries
James
how do on know that marketing is going on
Mutia
what is consumption
Raj
Using revenue
Prince
What is stock market
Prince
What are the marmet function
Odirile Reply
price elasticity of demand is the degree of responsiveness of a quantity demanded to the change in price of the commodity in question.
Gladys Reply
What does elasticity mean
Prince
Elasticity means change in demand with the change in price. It is elastic if the demand changes with the price change whereas it is inelastic if the demand is not affected due to change in price
Devesh
Okay
Olatunde
meaning
KP
okay
Binta
I have a question
Binta
what is the importance of learning economics?
Thelma Reply
it helps to make the correct choice
Gladys
it helps firm to produce products that will bring more profit
Gladys
the difference between needs and wants
londiwe Reply
needs are things that we basically can't live without wants are just luxury things
Thelma
needs are things without them we can't live but want are things without we can live
KP
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KP
it's a process in which we give or receiving methodical instructions
Thelma
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Amex
what is a deadweight loss? how monopoly creates a deadweight loss?
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Cleaford
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nura
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Lamine
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taiwo Reply
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Aarif Reply
what is demand schedle
Princess Reply
When you make a Scedule of the demand you made
Rodeen
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Prema Reply
What is macroeconomics
Kauna Reply
It's one of the two branches of Economics that deal with the aggregate economy.
Mayen
it's about inflation, occupation, gdp and so on
alberto
What is differences between Microeconomics and Macroeconomic?
Bethrand
microeconomics focuses on the action of individual agents in the economy such as businesses, workers and household. while macroeconomics looks at the economy as a whole. it focuses on broad issues in the economy such as government deficit, economy growth, levels of exports and imports, and
Thelma
inflationary increase in prices
Thelma
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Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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